Signum Function

Algebra Level 3

The signum function is defined to be \(\text{sgn}(x)=1,0,-1\) if \(x>0\), \(x=0\) and \(x<0\) respectively. Find the number of solutions of the equation \(x(x-3\text{sgn}(x))+\text{sgn}^2(x)=0\)

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